WEEK #4 ASSIGNMENT. NOTE: The first thing we will do this week is to learn how to use the regression results from EViews to make predictions.

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1 University of Canterbury Professor Bob Reed ECON 213 Second Semester 2009 WEEK #4 ASSIGNMENT NOTE: We will spend the next two weeks working through the material in Chapter 5. In case you are worried, we will go back and do Chapter 4 at a later date. DUE: Monday, August 3 rd Do the following exercises: NOTE: The first thing we will do this week is to learn how to use the regression results from EViews to make predictions. 1A. Read the top section of page 25 of the textbook to remind yourself how to obtain predicted values of the dependent variable using estimated regression results. 1B. Review Questions #11-13 from the Week #2 Assignment. 1C. Use the DVDData workfile you saved in your WEEK2 folder to re-estimate the regression model: DVDEXP = B 0 + B 1 INCOME + B 2 PRICE + B 3 RAINFALL + e. Compare your results with the estimates in TABLE 2-B on page 23 of the textbook. Your equation window should look like the one below: 1

2 1D. The first step in using EViews to calculate predicted values is to change the view in the Equation window from Estimation Output to Representations. To do that, click on the View button in the Equation window and select Representations. Your Equation window should now appear as follows: Next, cut and paste the estimated regression results below Estimation Equation: and paste them into the Command Window, which is the white work area located at the top of the Eviews workfile window (see below): Refer back to Question #11 in the Week #2 Assignment. In that question, you were asked to predict the value of DVDEXP when INCOME = 504, PRICE = 18.99, and RAINFALL =

3 Go back to your Command Window and substitute the number 504 for INCOME, for PRICE, and 1.9 for RAINFALL. Your Command Window should now look like the following: Type scalar at the beginning of the line and change DVDEXP to PRED1 (for prediction #1). Now your Command Window should look like this: Put your cursor at the end of the Command Window line and hit the enter key on your keyboard. The bottom of your EViews window should respond by stating PRED1 successfully created (see below). 3

4 Your Workfile window should now have a scalar object added to the other objects, so that it looks like the following (cf. pred1 ). To see what this value is, double-click on the pred1 object. Your predicted value will be listed at the bottom of the Workfile window where it will say PRED1 = (see below). That s your answer! Consider now Question #12 from the Week #2 Assignment. In this question you were asked to predict the value of DVDEXP for a different set of values: INCOME = 1000, PRICE = 20, and RAINFALL = 5. Go back to the Command Window and (i) change the values of the explanatory variables to these new values, and (ii) change the name of the scalar variable you are creating to PRED2 (for prediction #2). Your new Command Window should look like the following (see below): 4

5 Submit this command line by hitting Enter. Confirm that the new scalar variable PRED2 was successfully created, and its value is (see below). 1E. Sometimes it is useful to obtain the predicted value of the dependent variable for the case when all the explanatory variables take on their average values. This exercise demonstrates how you can do this. 5

6 From the Eviews Workfile window, select Quick / Group Statistics / Descriptive Statistics / Common sample. A Series List dialog box should appear. Type in the names of the explanatory variables -- income price rainfall so that your Series List dialog box looks like the one below: Click OK. The following Group window should appear. Click on the cell that displays the mean value of income (= ) and copy this cell by using the Edit / Copy option on the EViews taskbar (or by hitting the combination Ctrl + C on your keyboard). Paste this into the income variable in the Command Window. Repeat this process for the variables PRICE and RAINFALL. Change the name of the predicted variable to pred3. Your updated Command Window workspace should now look as follows: 6

7 Submit this command line by hitting Enter. Confirm that the new scalar variable PRED3 was successfully created, and its value is Exit Eviews and save your updated workfile into your WEEK4 folder. 2A. Read pages of Chapter 5 in the textbook. 2B. Answer Questions #1-4. 3A. (Estimate the Professional Wrestling Model of TABLE 5-B on page 88.) Create a folder on your P: drive called WEEK4. Download the Excel spreadsheet file Wrestle from the course website: Courses/ECON_213/Week4/index.html and save it into your WEEK4 folder. The data set Wrestle consists of 20 observations. After you download the EXCEL spreadsheet, take a look at the data and compare it with TABLE 5-A on page 87 of the text. Create a new EViews workfile, and import the Wrestle data into this workfile. Name the new workfile Wrestle and save it into your WEEK4 folder. Estimate the regression model of Equation (5-1) on page 86. Compare your regression results with those of TABLE 5-B on page 88 and confirm that you obtain the same estimates. Name the associated regression object EQ1. 3B. Answer Questions #

8 4A. (Transforming an existing variable with EViews.) This exercise demonstrates how EViews can be used to create a new variable from an existing one. Rather than using the dummy variable MALE, we will work with another dummy variable called FEMALE. Female will take the value 1 if a person is a female; and take the value 0 otherwise. Note that FEMALE = 1 - MALE. To create the variable FEMALE, go to Command Window and type in the following line: genr female = 1 - male Genr is the usual EViews command to create new variables. Your Command Window should look like the following Place your cursor at the end of the line and hit the enter key on your keyboard. You should notice that your workfile window now contains an object called female (see below). 8

9 Before proceeding, let s double-check to make sure we have correctly generated the new variable. Click on the objects female and male. Then click on the Workfile button called Show. A Show dialog box should appear like the one below: Click OK. A Group window will open up, displaying the individual values of these two variables (see below). You should be able to determine that, indeed, FEMALE = 1 MALE. 4B. Answer Question #11. 9

10 5A. Estimate the following regression model: HOURS = B 0 + B 1 FEMALE + B 2 INCOME + B 3 AGE + e. Save your regression results by naming the associated regression object EQ2. 5B. Answer Questions # A. (Estimate the Seasonal Retail Sales Model of TABLE 5-D on page 92.) Download the Excel spreadsheet file Retail from the course website: Courses/ECON_213/Week4/index.html and save it into your WEEK4 folder. The data set Retail consists of 22 observations. After you download the EXCEL spreadsheet, take a look at the data and compare it with TABLE 5-C on page 91 of the text. Note that I have added an additional dummy variable called SPRING. 6B. (Creating an EViews Workfile when the observations are dated.) In this exercise, you will create a new EViews workfile and import the Retail data into this workfile. The twist this time is that the data are dated. That is, rather than each observation being denoted by an observation or person number, each observation has a date associated with it, such as 1995:1 (= the first quarter of 1995), 1995:2 (= the second quarter of 1995), and so on. Begin by starting up EViews and select File/New/Workfile from the Main Menu. A dialog box will appear. Under Workfile structure type, choose Dated regular frequency from the drop down menu. Under Date specification enter (i) Quarterly in the box next to Frequency:, (ii) 1995:1 next to Start Date ; and (iii) 2000:2 next to End date: (see below): Click OK. Proceed in the usual fashion to import the EXCEL file Retail. Note that when the Excel Spreadsheet Import dialog box appears, you 10

11 should enter the number 7 where it says Names for series or Number if named in file (do you know why?). Save your workfile under the name Retail in your WEEK4 folder. If you have completed all these steps successfully, your workfile should look like the one below: You might want to use the Show button to check the variables SPRING through WINTER to make sure that everything is correct. 6C. Estimate the following regression model: SALES = B 0 + B 1 UNEMPLOY + B 2 SPRING + B 3 SUMMER + B 4 FALL + e. Save your regression results by naming the associated regression object EQ1. 6D. Answer Questions # E. Estimate the following regression model: SALES = B 0 + B 1 UNEMPLOY + B 2 SPRING + B 3 FALL + B 4 WINTER + e. Save your regression results by naming the associated regression object EQ2. 6F. Answer Questions # A. Re-read the section on Slope Dummies on pages 90f. in the text. 7B. (How to Create Slope Dummies Using EViews.) Open up the EViews workfile Wrestle that you last used in Exercise #5A. We want to create a slope dummy variable by multiplying the dummy variable MALE and the continuous variable INCOME. The new variable will be called MALExINCOME. 11

12 In the Command Window work area, type the following: genr malexincome = male*income Note that the * sign means multiply. When you are done, your updated workfile should display the new variable malexincome (see below). Use the Show command to check that this variable has been constructed correctly. 7C. Estimate the following regression model: HOURS = B 0 + B 1 MALE + B 2 INCOME + B 3 AGE + B 4 MALExINCOME + e. Save your regression results by naming the associated regression object EQ3. 7D. Answer Questions #

13 Be prepared to answer the following questions in class: 1. (Multiple choice: Select the single best answer.) Dummy variables are used to represent variables that are not numerical, such as a person s gender. A) True. B) False. 2. (Multiple choice: Select the single best answer.) Dummy variables typically take the values 1 and 0. A) True. B) False. 3. (Multiple choice: Select the single best answer.) Pages 86f. of the textbook present regression results for a study of the factors that affect the number of hours people spend watching professional wrestling on TV. Equation (5-2) on page 87 reports the following estimated regression equation using data from 20 men and women: HOURS = MALE INCOME AGE The estimated coefficient for the variable MALE is The best interpretation of this number is: A) Men watch an average of 4.47 hours of professional wrestling per month. B) Compared to women, men watch an average of 4.47 additional hours of professional wrestling per month. C) Both of the above. D) None of the above. 4. (Multiple choice: Select the single best answer.) Suppose we used the same observations from the preceding problem except that, instead of the dummy variable MALE, we created the dummy variable FEMALE, where FEMALE = 1 if a person is female; and FEMALE = 0 otherwise. You should be able to convince yourself that the corresponding estimated regression equation would be: HOURS = FEMALE INCOME AGE The estimated coefficient for the variable FEMALE is The best interpretation of this number is: A) Compared to men, women watch an average of 4.47 fewer hours of professional wrestling per month. B) Compared to women, men watch an average of 4.47 additional hours of professional wrestling per month. C) Both of the above. D) None of the above. 13

14 5. (Supply the correct numerical answer on the line below.) Use the regression results from Exercise #3A to predict the number of monthly viewing hours for a 40 year-old female with an annual income of $50,000. Write your answer below: 6. (Supply the correct numerical answer on the line below.) Use the regression results from Exercise #3A to predict the number of monthly viewing hours for a 40 year-old male with an annual income of $50,000. Write your answer below: 7. (Supply the correct numerical answer on the line below.) Use your answers from the two previous questions to answer the following: On average, how many more hours of professional wrestling does a 40 yearold male with an annual income of $50,000 watch, compared to a woman of the same age and income? Write your answer below: 8. (Supply the correct numerical answer on the line below.) Use the regression results from Exercise #3A to predict the number of monthly viewing hours for a female with average characteristics (i.e., a female having average values of INCOME and AGE). Write your answer below: 9. (Supply the correct numerical answer on the line below.) Use the regression results from Exercise #3A to predict the number of monthly viewing hours for a male with average characteristics (i.e., a male having average values of INCOME and AGE). Write your answer below: 10. (Supply the correct numerical answer on the line below.) Use your answers from the two previous questions to answer the following: On average, how many more hours of professional wrestling does a male of average age and income watch, compared to a woman of average age and income? Write your answer below: 14

15 11. (Supply the correct numerical answer on the line below.) What is the average (mean) value of the variable FEMALE? Write your answer below: 12. (Supply the correct numerical answer on the line below.) Use the regression results from Exercise #5A to predict the number of monthly viewing hours for a 40 year-old female with an annual income of $50,000. Write your answer below: 13. (Supply the correct numerical answer on the line below.) Use the regression results from Exercise #5A to predict the number of monthly viewing hours for a 40 year-old male with an annual income of $50,000. Write your answer below: 14. (Supply the correct numerical answer on the line below.) Use your answers from the two previous questions to answer the following: On average, how many more hours of professional wrestling does a 40 yearold male with an annual income of $50,000 watch, compared to a woman of the same age and income? Write your answer below: 15. (Provide a short answer in the space below.) Estimate the following regression model: HOURS = B 0 + B 1 FEMALE + B 2 MALE + B 3 INCOME + B 4 AGE + e. How does EViews respond when you try and estimate this model? 16. (Provide a short answer in the space below.) In plain English, briefly explain why EViews is not able to estimate the model: HOURS = B 0 + B 1 FEMALE + B 2 MALE + B 3 INCOME + B 4 AGE + e. 15

16 17. (Multiple choice: Select the single best answer.) Consider the Seasonal Retail Sales Model on page 89 of the textbook. We want to estimate the relationship between Retail Sales and the season of the year, among other things. There are four seasons: SUMMER, FALL, WINTER, SPRING. Assuming there is also a constant term, what is the maximum number of seasonal dummy variables you can include in this regression model? A) 4. B) 3. C) 2. D) (Supply the correct numerical answer on the line below.) What is the estimated value of the coefficient for the variable SPRING that you estimated in Exercise #6C? 19. (Provide a short answer in the space below.) In plain English, provide a brief interpretation of the number you reported in the question above. 20. (Supply the correct numerical answer on the line below.) Use the regression results from Exercise #6C to predict real U.S. quarterly retail sales for the winter season when unemployment is 5%. Write your answer below: 21. (Supply the correct numerical answer on the line below.) What is the estimated value of the coefficient for the variable SPRING that you estimated in Exercise #6E? 22. (Provide a short answer in the space below.) In plain English, provide a brief interpretation of the number you reported in the question above. 16

17 23. (Supply the correct numerical answer on the line below.) Use the regression results from Exercise #6E to predict real U.S. quarterly retail sales for the winter season when unemployment is 5%. Write your answer below: 24. (Multiple choice: Select the single best answer.) Compare your answers to Questions #20 and #23. Are they the same? A) Yes. B) No. 25. (Multiple choice: Select the single best answer.) The document QuickStats About Culture and Identity 2006 Census from Statistics New Zealand 1 lists the following ethnic groups in New Zealand: (i) European, (ii) Maori, (iii) Asian, (iv) Pacific peoples, (v) MELAA (=Middle Eastern, Latin American, and African), and (vi) Other. Assuming there is also a constant term, what is the maximum number of ethnic group dummy variables you could include in a regression model using ethnic group data from Statistics New Zealand? A) 6. B) 5. C) 1. D) None of the above. 26. (Multiple choice: Select the single best answer.) Your regression results from Exercise #7C should show an estimated coefficient for MALE equal to 8.66, and an estimated coefficient for MALExINCOME equal to The best interpretation of this latter number is: A) While men generally watch more professional wrestling than women, the gap is smaller for higher-income men and women, compared to lower-income men and women. B) Men generally watch more professional wrestling than women, and the gap is larger for higher-income men and women, compared to lower-income men and women C) High income males watch less professional wrestling than low-income males. D) None of the above. 1 You don t have to read it, but if you are interested in looking at it, it can be found at the following URL: quickstatsaboutcultureandidentity.pdf. 17

18 27. (Supply the correct numerical answer on the line below.) Use the regression results from Exercise #7C to predict the number of monthly viewing hours for a 40 year-old female with an annual income of $20,000. Write your answer below: (HINT: The value of MALExINCOME in this case equals 0 x = 0.) 28. (Supply the correct numerical answer on the line below.) Use the regression results from Exercise #7C to predict the number of monthly viewing hours for a 40 year-old male with an annual income of $20,000. Write your answer below: (HINT: The value of MALExINCOME in this case equals 1 x = ) 29. (Supply the correct numerical answer on the line below.) Use your answers from the two previous questions to answer the following: On average, how many more hours of professional wrestling does a 40 yearold male with an annual income of $20,000 watch, compared to a woman of the same age and income? Write your answer below: 18